"The warmest coat is a little drink of Cognac" — well, doesn't seem to make much sense. But that's because the pun is lost in translation.

Of course this is about the "warming" effect (also figuratively, i.e. causing social comfort) of alcohol. For example, if I enter a house as a guest in cold winter weather and they offer me a drink I might thankfully ackknowlegde that with a smile and that saying. It is to mean that I need to warm up from the cold outside and might do so by dressing warm (i.e. keeping my coat on) or I happily prefer to have a drink with my hosts, which is at least as pleasent and helpful.

This is a pun (German: "Wortwitz"). Whereas admittedly I have never ever heard it in its diminutive form. Also even though it rhymes, the plural form is the one I'm accustomed to:

Die wärmsten Jacken sind die Kognak-en

Where "Kognak" is an allowed spelling of "cognac". It's a pun because it rhymes "Jacken" (plural of jacket/coat, obvious cognate of jacket) with a modified version of "Kognak", appending "-en", because if you were to spell out the German pronunciation in German it would be something like "Konjack" (short "a", hard "k") and therefore fits nicely.